The Graph

Time to get in the weeds, and when I say “weeds” I mean numbers.

I’ve added the following graph to the Purchase Speaker Hardware Bundles page. The graph aids in visualizing how increasing the number of well-placed metronome speakers drastically reduces relative delay between musicians. The following data showing percentages of a football field covered by ranges of relative delay is graphed.

1 Speaker 2 Speakers 3 Speakers 4 Speakers 5 Speakers 6 Speakers
<5 milli-seconds 9.01% 35.58% 51.61% 55.48% 65.89% 76.91%
5><20 milli-seconds 10.88% 35.58% 33.81% 29.35% 25.25% 20.99%
20><40 milli-seconds 11.98% 22.10% 13.70% 10.19% 6.42% 2.10%
>40 milli-seconds 68.13% 6.74% 1.33% 4.98.% 2.44% 0.00%

Here’s the graph.

relative delay chart

So what does all this mean?

Well first, a few caveats. Like the data on the Purchase Hardware page, these data assume:

  • an air temperature of 82 F, *
  • a sweet spot on the 50 yard line and 56 feet forward of the front sideline, and
  • an arc width of 114 degrees. **

Generally this means that more speakers increase overall speaker array performance, particularly on the parts of the field where the musicians play — the power zone.

If you take a close look at the numbers in each delay range, the numbers do not necessarily change linearly. This is partly due to how much space on or beyond a practice field is available or necessary for odd numbers vs. even numbers of speakers. So generally, the further away we can place the speakers, the better the array performance. I should mention here that Anchor Audio speaker volume is not to be worried about. Their speakers are plenty loud and can easily overwhelm the largest marching ensembles for rehearsal on the field.

This shows that the current technique of placing one speaker right behind the battery dramatically increases relative delay on the field as demonstrated in the following example from the 2013 Cavaliers program.

2017-10-04 11.38.47.jpg
2013 Cavaliers blocking.

This moment from the 2013 Cavaliers is pretty close to a worst-case scenario. Rehearsing with a metronome placed just behind the bass drums, the current technique, leaves the trumpet players in the far-right corner of the field with more than a 10th of a second delay as demonstrated in the following model.

Screen Shot 2017-10-05 at 15.18.06.png
A portion of a football field with the above staging highlighted mapping the relative delay in milliseconds from musicians standing in 4 step by 4 step grid cells playing exactly with one metronome speaker placed at the red A to a person standing on the red x . ***

I can customize a speaker placement coordinate set for a specific section of drill where the blocking (staging) is particularly challenging like this. Such a speaker placement set would provide a teachable, objective metronome reference that reduces relative delay to less than five thousandths of a second for every marching musician on the field.

Screen Shot 2017-10-05 at 19.24.52.png
A portion of a football field with the above staging highlighted mapping the relative delay in milliseconds from musicians standing in 4 step by 4 step grid cells playing exactly with six metronome speakers per the EncelaPulse technique.


Our students deserve this.

Let’s take a look at the relative delay for a three-speaker array.

Screen Shot 2017-10-05 at 09.24.47.png
A portion of a football field mapping the relative delay in milliseconds to a person standing on the 50 yard line and 56 feet forward of the front sideline with on-field musicians playing exactly with three metronome speakers per the EncelaPulse technique.

Notice that with only three well-placed speakers, more than half the field has a delay of less than five millisecond (that’s less than 5 thousandths of a second), and most of that area is inside the 20s and forward of the back hash.

A six-speaker array greatly increases the less than 5 and less than 20 millisecond areas of relative delay.

Screen Shot 2017-10-05 at 08.50.53

Anyone who made it this far is a true geek, a real trooper, or some combination of both. Many thanks to you. I welcome your respectful comments and questions.

In conclusion…

My thesis is that the current metronome techniques are inadequate and outdated because they do not provide proper phase adjustment due to distances between musicians. I believe EncelaPulse is a reasonably practical and affordable way to provide students with teachable, objective, metronome pulses that correct for distances between musicians.

* Higher air temperatures reduce relative delay. Lower temperatures increase relative delay. Barometric pressure has no effect on relative delay.

** The sweet spot distance and arc width are what the Lafayette High School Band is currently (fall of 2017) using. Their rehearsal tower is about 56 feet from the front sideline. They are marching 64 winds and 64 brass with additional battery percussion and sousaphones. Their drill design covers almost the whole field. There is no arc coverage with only one speaker.

*** For modeling relative delay I modified a spreadsheet created by Steven Finn, a solid friend, musician, and engineer at any temperature. Each cell is 4 steps by 4 steps. Field markings run through the middle of the cells. College hashes are depicted, and an area for the front ensemble between the 20s is included. The number in each cell shows the relative delay from musicians standing in that cell to a person standing in the sweet spot. The musicians standing in the cells marked “0” will sound first, musicians standing in non-zero cells will sound that many milliseconds later.

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